In this paper, we consider a ring neural network with one-way distributed-delay coupling between the neurons and a discrete delayed self-feedback. In the general case of the distribution kernels, we are able to find a subset of the amplitude death regions depending on even (odd) number of neurons in the network. Furthermore, in order to show the full region of the amplitude death, we use particular delay distributions, including Dirac delta function and gamma distribution. Stability conditions for the trivial steady state are found in parameter spaces consisting of the synaptic weight of the self-feedback and the coupling strength between the neurons, as well as the delayed self-feedback and the coupling strength between the neurons. It is shown that both Hopf and steady-state bifurcations may occur when the steady state loses stability. We also perform numerical simulations of the fully nonlinear system to confirm theoretical findings.

中文翻译：

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具有离散和分布时滞的单向耦合环神经网络的动力学。

在本文中，我们考虑了一个环形神经网络，在神经元之间具有单向分布式延迟耦合，并具有离散的延迟自反馈。在分布核的一般情况下，我们能够根据网络中神经元的偶数（奇数）找到幅度死亡区域的子集。此外，为了显示振幅死亡的整个区域，我们使用了特定的延迟分布，包括狄拉克δ函数和伽马分布。在由自反馈的突触权重和神经元之间的耦合强度以及延迟的自反馈和神经元之间的耦合强度组成的参数空间中，可以找到微不足道的稳定状态的条件。结果表明，当稳态失去稳定性时，Hopf和稳态分叉都可能发生。